Well educated as they are, skilled people usually don't prefer to live illegally. And that's why you will most likely see ex-illegals and unskilled people receiving green cards or citizenship in US.
Do you mean being arrested? Because having your permission to stay/work revoked with a given time to leave the country looks like being deported for me. After that, even a touristic visa will be harder to obtain again.
Please, don't get offended. I'm not a heavy user here and I don't have permission to downvote posts.
"Told to leave"; sure he could stay an illegal and just live off the radar, but the expected value of that is really low given his options anywhere else in the world. I guess if you want to argue semantics, his risk of being physically flown out of the country was probably not substantial.
I think the purpose of all this discussion was whether OP should come to the States and work under the radar, and the general consensus is that being here illegally strongly caps your upside, and has a pretty uncertain downside.
PS - My friend's now the chief engineer of a successful business in London... I always thought it was such a shame for a guy who worked his way from being an orphan on a farm in Kenya to live 90% of the American Dream, only to be kicked out of the country after putting in his all at Stanford and at a few startups.